thesis variational methods

In this thesis, we study variational inference as a framework for meeting these challenges. An introductory chapter motivates the use of stochastic processes as priors, with a ... On Sparse Variational methods and the Kullback-Leibler divergence between stochastic processes. In 19th International Conference on Artificial Intelligence and ...

usually discontinuous and thus the connection of the variational problem to the PDE is much more complicated, requiring weak convergence methods and geometric measure theory. The plan of this dissertation is to work out the mathematical background required to deal with these classes of problems. First we discuss formally some main results of

Two fundamental examples of such variational principles are due to Fermat and Hamilton. Fermat's Principle Consider a light ray passing through a medium of variable refractive index µ(r). The path it takes between two fixed points A and B is such as to minimise the optical path length Z B A µ(r)dl, where dl is the length of a path element.

7.2 Summary of contributions. The aim of this thesis has been to investigate the variational Bayesian method for approximating Bayesian inference and learning in a variety of statistical models used in machine learning ap-plications. Chapter 1 reviewed some of the basics of probabilistic inference in graphical models, such as the junction tree ...

In this thesis, we implement a new analytical technique, the He's variational iteration method for solving two types of differential equations: *A nonlinear ordinary boundary value problem ...

The variational iteration method (VIM) [18-21], which is a well-established technique with wide applications for ordinary differential equations, partial differential equations and delay differential equations, etc. More materials of the classical solution techniques that are most commonly used to solve equations and

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 1997. Includes bibliographical references. ... Variational methods for inference and estimation in graphical models. Author(s) Jaakkola, Tommi S. (Tommi Sakari) DownloadFull printable version (7.881Mb) Advisor.

The contribution of this thesis, then, is twofold: first, we uncover two sources of bias in existing variational inference methods applied to dynamical systems in general, and state space models whose transition function is drawn from a Gaussian process (GPSSM) in particular. We show bias can derive from assuming posteriors in non-linear ...

In 1997, in his Ph.D. Thesis, He proposed a novel method called the semi-inverse method to search for variational formulations directly from field equations and boundary conditions without a Lagrange multiplier (He 1997b, c). In 1998, the well-known variational iteration method (VIM) was suggested by using general

The variational iteration method (VIM) is one of the well-known semi-analytical methods for solving linear and nonlinear ordinary as well as partial differential equations. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily. The method can be used in bounded and unbounded domains as well.

This thesis proposes a principled framework for approximating graphical models based on variational methods and develops variational techniques from the perspective that unifies and expands their applicability to graphical models. Graphical models enhance the representational power of probability models through qualitative characterization of their properties.

The purpose of this dissertation is to present a scheme where the current numerical methods can be benchmarked in a qualitative as well as in a quantitative manner. It is shown how different combinations of methods, even for a simple model, can give very different results, particularly in the field of dynamics, where often also instabilites arise.

The variational iteration method has been favored by many, and thus applied to several different types of nonlinear problems. The primary property of this method lies in its capability and flexibility in accurately and appropriately solving nonlinear equations. Furthermore, it was recently noted that the variational iteration method, as well as other analytical methods, is considered as ...

The Variational Iteration Method (VIM) [24,25,27] which was introduced by Chinese mathematician J.H. He in 1997 is one of the methods that obtains approximate solu-tions of differential equations. This method is a modification of the general Lagrange multiplier method which was proposed by Inokuti et al. in 1978 [30]. The key ele-

Variational Bayesian Theory 2.1 Introduction This chapter covers the majority of the theory for variational Bayesian learning that will be used in rest of this thesis. It is intended to give the reader a context for the use of variational methods as well as a insight into their general applicability and usefulness.

The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients This in turn gives the successive approximations u 0 ( x ) = 1 − 1

The second part of this thesis is devoted to the so-called Weighted-Inertia-Dissi-pation-Energy principle (abbreviated WIDE principle in the following). The WIDE ... by functionals using variational methods such as Γ-convergence, see [SaS04, AM ...

This thesis presents a variety of new, continuous, Bayesian Gaussian-process-driven Cox process models used to model sparse event data distributed on a continuous domain, and presents the first known variational inference scheme for such models, which scales linearly with the size of the dataset.

In this thesis we present a variational approach to surface parameterization that addresses these challenges. The first contribution of this thesis is the development of a variational framework for parameterizations. ... Nathan Jacob (2005) Variational Methods in Surface Parameterization. Dissertation (Ph.D.), California Institute of Technology ...

Variational Methods for Energy Systems. ... in this thesis, we introduce an auxiliary distribution that can theoretically approximate any distribution over binary states arbitrarily well. Furthermore, in the case of Non-Intrusive Load Monitoring, because the problem requirestracking appliance states over time and modeling temporal dependencies ...

Variational iteration method (VIM) Where p( ) 3 c 2 2303 (8) VIM is the general Lagrange method, in which an extremely accurate approximation at some special point can be obtained, but not an analytical solution. To illustrate the basic idea of the VIM we consider the following general partial differential equation: Lt u( x, t ) Lx u( x, t ) N ...

In this thesis, we use the variational iteration technique and its various modifications to suggest and analyze several iterative methods for finding the approximate solution of the nonlinear equations. Using suitable finite difference schemes, a number of new iterative methods free from second derivative are considered and analyzed ...

In this thesis, we provide a new modification of the variational iteration method (MVIM) for solving van der Pol equations. The modification couples the classical variational iteration method with He's polynomials, where the He's polynomials are applied to the approximate solution and the initial condition to eliminate secular terms.

View a PDF of the paper titled Variational Inference for Acceleration of SN Ia Photometric Distance Estimation with BayeSN, by Ana Sof\'ia M. Uzsoy and 3 other authors. ... we show that VI is a promising method for scalable parameter inference that enables analysis of larger datasets for precision cosmology. Comments: 14 pages, 7 figures, 1 ...

Variational Schrodinger Diffusion Models¨ Wei Deng* 1 Weijian Luo* 2 Yixin Tan* 3 Marin Biloˇs 1Yu Chen Yuriy Nevmyvaka1 Ricky T. Q. Chen4 Abstract Schrodinger bridge (SB) has emerged as the go-to¨ method for optimizing transportation plans in dif-fusion models. However, SB requires estimating the intractable forward score functions, inevitably

We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method is applied to find the saddle-node bifurcation point for elliptic equations with the nonlinearity of the general convex-concave type. The main result justifies the variational formula for the detection of the ...

Original lidar return signals are covered by high levels of noise that seriously affect the accuracy of subsequent data processing and inversion. Therefore, it is important to separate the effective signal from the returned signal with noise interference. In this paper, an efficient denoising method based on the variational mode decomposition (VMD) algorithm optimized using the global search ...